An Introduction to Information Theory

Symbols, Signals and Noise

Author: John R. Pierce

Publisher: Courier Corporation

ISBN: 0486134970

Category: Computers

Page: 336

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Covers encoding and binary digits, entropy, language and meaning, efficient encoding and the noisy channel, and explores ways in which information theory relates to physics, cybernetics, psychology, and art. 1980 edition.

An Introduction to Information Theory

Author: Fazlollah M. Reza

Publisher: Courier Corporation

ISBN: 0486158446

Category: Mathematics

Page: 528

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Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.

Information Theory

Part I: An Introduction to the Fundamental Concepts

Author: Arieh Ben-Naim

Publisher: World Scientific

ISBN: 9813208821

Category: Computers

Page: 220

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This book is about the definition of the Shannon measure of Information, and some derived quantities such as conditional information and mutual information. Unlike many books, which refer to the Shannon's Measure of information (SMI) as "Entropy," this book makes a clear distinction between the SMI and Entropy. In the last chapter, Entropy is derived as a special case of SMI. Ample examples are provided which help the reader in understanding the different concepts discussed in this book. As with previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in Information theory — the Shannon's Measure of Information. This book presents the fundamental concepts of Information theory in a friendly-simple language and is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject. It is unique in its presentation of Shannon's measure of information, and the clear distinction between this concept and the thermodynamic entropy. Although some mathematical knowledge is required by the reader, the emphasis is on the concepts and their meaning rather on the mathematical details of the theory.

Introduction to Coding and Information Theory

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 9780387947044

Category: Computers

Page: 323

View: 8191

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This book is an introduction to coding theory and information theory for undergraduate students of mathematics and computer science. Among the topics it discusses are: a review of probablity theory; the efficiency of codes, the capacity of communications channels, coding and decoding in the presence of errors, the general theory of linear codes, and examples of specific codes used in ordinalry communications as wwell as cryptography.

Information Theory

A Tutorial Introduction

Author: JV Stone

Publisher: Sebtel Press

ISBN: 0956372856

Category: Information theory

Page: 243

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Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.

Mathematical Foundations of Information Theory

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486604343

Category: Mathematics

Page: 120

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First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

Introduction to Information Theory and Data Compression, Second Edition

Author: Peter D. Johnson, Jr.,Greg A. Harris,D.C. Hankerson

Publisher: CRC Press

ISBN: 9781420035278

Category: Mathematics

Page: 384

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An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed so that the data compression section requires no prior knowledge of information theory. The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory, the authors then apply the theory to memoryless, discrete channels with zeroth-order, one-state sources. The chapters on data compression acquaint students with a myriad of lossless compression methods and then introduce two lossy compression methods. Students emerge from this study competent in a wide range of techniques. The authors' presentation is highly practical but includes some important proofs, either in the text or in the exercises, so instructors can, if they choose, place more emphasis on the mathematics. Introduction to Information Theory and Data Compression, Second Edition is ideally suited for an upper-level or graduate course for students in mathematics, engineering, and computer science. Features: Expanded discussion of the historical and theoretical basis of information theory that builds a firm, intuitive grasp of the subject Reorganization of theoretical results along with new exercises, ranging from the routine to the more difficult, that reinforce students' ability to apply the definitions and results in specific situations. Simplified treatment of the algorithm(s) of Gallager and Knuth Discussion of the information rate of a code and the trade-off between error correction and information rate Treatment of probabilistic finite state source automata, including basic results, examples, references, and exercises Octave and MATLAB image compression codes included in an appendix for use with the exercises and projects involving transform methods Supplementary materials, including software, available for download from the authors' Web site at www.dms.auburn.edu/compression

An Introduction to Single-User Information Theory

Author: Fady Alajaji,Po-Ning Chen

Publisher: Springer

ISBN: 9811080011

Category: Mathematics

Page: 323

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This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon’s information theory, discussing the fundamental concepts and indispensable results of Shannon’s mathematical theory of communications. It includes five meticulously written core chapters (with accompanying problems), emphasizing the key topics of information measures; lossless and lossy data compression; channel coding; and joint source-channel coding for single-user (point-to-point) communications systems. It also features two appendices covering necessary background material in real analysis and in probability theory and stochastic processes. The book is ideal for a one-semester foundational course on information theory for senior undergraduate and entry-level graduate students in mathematics, statistics, engineering, and computing and information sciences. A comprehensive instructor’s solutions manual is available.

Codes: An Introduction to Information Communication and Cryptography

Author: Norman L. Biggs

Publisher: Springer Science & Business Media

ISBN: 9781848002739

Category: Computers

Page: 274

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Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Coding and Information Theory

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 9780387978123

Category: Mathematics

Page: 488

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This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.

Information Theory and Statistics

Author: Solomon Kullback

Publisher: Courier Corporation

ISBN: 0486142043

Category: Mathematics

Page: 416

View: 8519

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Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.

Elements of Information Theory

Author: Thomas M. Cover,Joy A. Thomas

Publisher: John Wiley & Sons

ISBN: 1118585771

Category: Computers

Page: 792

View: 9634

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The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Classical and Quantum Information Theory

An Introduction for the Telecom Scientist

Author: Emmanuel Desurvire

Publisher: Cambridge University Press

ISBN: 0521881714

Category: Science

Page: 691

View: 2338

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This complete overview of classical and quantum information theory employs an informal yet accurate approach, for students, researchers and practitioners.

Probability and Information

An Integrated Approach

Author: David Applebaum

Publisher: Cambridge University Press

ISBN: 9780521555289

Category: Computers

Page: 212

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This elementary introduction to probability theory and information theory provides a clear and systematic foundation to the subject; the author pays particular attention to the concept of probability via a highly simplified discussion of measures on Boolean algebras. He then applies the theoretical ideas to practical areas such as statistical inference, random walks, statistical mechanics, and communications modeling. Applebaum deals with topics including discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem, and the coding and transmission of information. The author includes many examples and exercises that illustrate how the theory can be applied, e.g. to information technology. Solutions are available by email. This book is suitable as a textbook for beginning students in mathematics, statistics, or computer science who have some knowledge of basic calculus.

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

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Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.